The fidelity function for quantum states has been widely used in quantum information science and frequently arises in the quantification of optimal performances for the estimation and distinguishing of quantum states. A fidelity function for quantum channels is expected to have the same wide applications in quantum information science. In this paper we propose a fidelity function for quantum channels and show that various distance measures on quantum channels can be obtained from this fidelity function; for example, the Bures angle and the Bures distance can be extended to quantum channels via this fidelity function. We then show that the distances between quantum channels lead naturally to a quantum channel Fisher information which quantifies the ultimate precision limit in quantum metrology; the ultimate precision limit can thus be seen as a manifestation of the distances between quantum channels. We also show that the fidelity of quantum channels provides a unified framework for perfect quantum channel discrimination and quantum metrology. In particular, we show that the minimum number of uses needed for perfect channel discrimination is exactly the counterpart of the precision limit in quantum metrology, and various useful lower bounds for the minimum number of uses needed for perfect channel discrimination can be obtained via this connection.

Various strategies exist in quantum metrology, such as with or without ancillary system, with a fixed or optimized measurement, with or without monitoring the environment, etc. Different set of tools are usually needed for different strategies. In this article, we provide a unified framework for these different settings, in particular we introduce a quantum metrology matrix and show that the precision limits of different settings can all be obtained from the trace or the trace norm of the quantum metrology matrix. Furthermore, the probe state enters into the quantum metrology matrix linearly, which makes the identification of the optimal probe states, one of the main quests in quantum metrology, much more efficient than conventional methods.

Quantum-key-distribution (QKD) networks are gaining importance and it has become necessary to analyze the most appropriate methods for their long-distance interconnection. In this paper, four different methods of interconnecting remote QKD networks are proposed. The methods are used to link three different QKD testbeds in Europe, located in Berlin, Madrid, and Poznan. Although long-distance QKD links are only emulated, the methods used can serve as a blueprint for the secure interconnection of distant QKD networks in the future. Specifically, the presented approaches combine, in a transparent way, different fiber and satellite physical media, as well as common standards of key delivery interfaces. The testbed interconnections are designed to increase the security by utilizing multipath techniques and multiple hybridizations of QKD and post-quantum cryptography (PQC) algorithms.

We present a demonstration of software defined networking (SDN) services utilizing quantum key distribution (QKD) technology, fully integrated with standard telecommunication network connecting production facilities of Telefonica in Madrid. All communications “co-propagate” over the same fiber infrastructure.

Nearest-neighbour clustering is a simple yet powerful machine learning algorithm that finds natural application in the decoding of signals in classical optical-fibre communication systems. Quantum k-means clustering promises a speed-up over the classical k-means algorithm; however, it has been shown to not currently provide this speed-up for decoding optical-fibre signals due to the embedding of classical data, which introduces inaccuracies and slowdowns. Although still not achieving an exponential speed-up for NISQ implementations, this work proposes the generalised inverse stereographic projection as an improved embedding into the Bloch sphere for quantum distance estimation in k-nearest-neighbour clustering, which allows us to get closer to the classical performance. We also use the generalised inverse stereographic projection to develop an analogous classical clustering algorithm and benchmark its accuracy, runtime and convergence for decoding real-world experimental optical-fibre communication data. This proposed ‘quantum-inspired’ algorithm provides an improvement in both the accuracy and convergence rate with respect to the k-means algorithm. Hence, this work presents two main contributions. Firstly, we propose the general inverse stereographic projection into the Bloch sphere as a better embedding for quantum machine learning algorithms; here, we use the problem of clustering quadrature amplitude modulated optical-fibre signals as an example. Secondly, as a purely classical contribution inspired by the first contribution, we propose and benchmark the use of the general inverse stereographic projection and spherical centroid for clustering optical-fibre signals, showing that optimizing the radius yields a consistent improvement in accuracy and convergence rate.

A monitor and control framework for quantum-key-distribution (QKD) networks equipped with switching capabilities was developed. On the one hand, this framework provides real-time visibility into operational metrics. Specifically, it extracts essential data, such as the switching capabilities of QKD modules, the number of keys stored in buffer queues of the QKD links, and the respective key generation and consumption rates along these links. On the other hand, this framework allows software-defined networking (SDN) applications to operate on the collected information and address the cryptographic needs of the network. The SDN applications dynamically adapt the configuration of the switched network to align with its changing demands, e.g., prioritizing key availability on critical paths, responding to link failures, or reallocating generation capacity to prevent bottlenecks. This contribution demonstrates that the combination of switched QKD, centralized control, and global optimization strategies enables efficient, policy-driven operation of QKD networks. The cryptographic resources are allocated to maximize performance and resilience while remaining aligned with the specific policies set by network administrators.